7L 7s

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Scale structure
Step pattern LsLsLsLsLsLsLs
sLsLsLsLsLsLsL
Equave 2/1 (1200.0 ¢)
Period 1\7 (171.4 ¢)
Generator size
Bright 1\14 to 1\7 (85.7 ¢ to 171.4 ¢)
Dark 0\7 to 1\14 (0.0 ¢ to 85.7 ¢)
Related MOS scales
Parent none
Sister 7L 7s (self)
Daughters 14L 7s, 7L 14s
Neutralized 14edo
2-Flought 21L 7s, 7L 21s
Equal tunings
Equalized (L:s = 1:1) 1\14 (85.7 ¢)
Supersoft (L:s = 4:3) 4\49 (98.0 ¢)
Soft (L:s = 3:2) 3\35 (102.9 ¢)
Semisoft (L:s = 5:3) 5\56 (107.1 ¢)
Basic (L:s = 2:1) 2\21 (114.3 ¢)
Semihard (L:s = 5:2) 5\49 (122.4 ¢)
Hard (L:s = 3:1) 3\28 (128.6 ¢)
Superhard (L:s = 4:1) 4\35 (137.1 ¢)
Collapsed (L:s = 1:0) 1\7 (171.4 ¢)

7L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 7 small steps, with a period of 1 large step and 1 small step that repeats every 171.4 ¢, or 7 times every octave. Generators that produce this scale range from 85.7 ¢ to 171.4 ¢, or from 0 ¢ to 85.7 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period. This scale appears as the whitewood chromatic scale.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

Intervals

Intervals of 7L 7s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 85.7 ¢
Major 1-mosstep M1ms L 85.7 ¢ to 171.4 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 171.4 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 171.4 ¢ to 257.1 ¢
Major 3-mosstep M3ms 2L + s 257.1 ¢ to 342.9 ¢
4-mosstep Perfect 4-mosstep P4ms 2L + 2s 342.9 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 342.9 ¢ to 428.6 ¢
Major 5-mosstep M5ms 3L + 2s 428.6 ¢ to 514.3 ¢
6-mosstep Perfect 6-mosstep P6ms 3L + 3s 514.3 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 514.3 ¢ to 600.0 ¢
Major 7-mosstep M7ms 4L + 3s 600.0 ¢ to 685.7 ¢
8-mosstep Perfect 8-mosstep P8ms 4L + 4s 685.7 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 685.7 ¢ to 771.4 ¢
Major 9-mosstep M9ms 5L + 4s 771.4 ¢ to 857.1 ¢
10-mosstep Perfect 10-mosstep P10ms 5L + 5s 857.1 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 857.1 ¢ to 942.9 ¢
Major 11-mosstep M11ms 6L + 5s 942.9 ¢ to 1028.6 ¢
12-mosstep Perfect 12-mosstep P12ms 6L + 6s 1028.6 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 1028.6 ¢ to 1114.3 ¢
Major 13-mosstep M13ms 7L + 6s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 7L + 7s 1200.0 ¢

Generator chain

Generator chain of 7L 7s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
2 Augmented 0-mosdegree A0md Augmented 2-mosdegree A2md Augmented 4-mosdegree A4md Augmented 6-mosdegree A6md Augmented 8-mosdegree A8md Augmented 10-mosdegree A10md Augmented 12-mosdegree A12md
1 Major 1-mosdegree M1md Major 3-mosdegree M3md Major 5-mosdegree M5md Major 7-mosdegree M7md Major 9-mosdegree M9md Major 11-mosdegree M11md Major 13-mosdegree M13md
0 Perfect 0-mosdegree
Perfect 2-mosdegree		 P0md
P2md		 Perfect 2-mosdegree
Perfect 4-mosdegree		 P2md
P4md		 Perfect 4-mosdegree
Perfect 6-mosdegree		 P4md
P6md		 Perfect 6-mosdegree
Perfect 8-mosdegree		 P6md
P8md		 Perfect 8-mosdegree
Perfect 10-mosdegree		 P8md
P10md		 Perfect 10-mosdegree
Perfect 12-mosdegree		 P10md
P12md		 Perfect 12-mosdegree
Perfect 14-mosdegree		 P12md
P14md
−1 Minor 1-mosdegree m1md Minor 3-mosdegree m3md Minor 5-mosdegree m5md Minor 7-mosdegree m7md Minor 9-mosdegree m9md Minor 11-mosdegree m11md Minor 13-mosdegree m13md
−2 Diminished 2-mosdegree d2md Diminished 4-mosdegree d4md Diminished 6-mosdegree d6md Diminished 8-mosdegree d8md Diminished 10-mosdegree d10md Diminished 12-mosdegree d12md Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 7L 7s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
7|0(7) 1 LsLsLsLsLsLsLs Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf. Maj. Perf.
0|7(7) 2 sLsLsLsLsLsLsL Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 7L 7s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\14 85.714 85.714 1:1 1.000 Equalized 7L 7s
6\77 93.506 77.922 6:5 1.200
5\63 95.238 76.190 5:4 1.250
9\112 96.429 75.000 9:7 1.286
4\49 97.959 73.469 4:3 1.333 Supersoft 7L 7s
11\133 99.248 72.180 11:8 1.375
7\84 100.000 71.429 7:5 1.400
10\119 100.840 70.588 10:7 1.429
3\35 102.857 68.571 3:2 1.500 Soft 7L 7s
11\126 104.762 66.667 11:7 1.571
8\91 105.495 65.934 8:5 1.600
13\147 106.122 65.306 13:8 1.625
5\56 107.143 64.286 5:3 1.667 Semisoft 7L 7s
12\133 108.271 63.158 12:7 1.714
7\77 109.091 62.338 7:4 1.750
9\98 110.204 61.224 9:5 1.800
2\21 114.286 57.143 2:1 2.000 Basic 7L 7s
9\91 118.681 52.747 9:4 2.250
7\70 120.000 51.429 7:3 2.333
12\119 121.008 50.420 12:5 2.400
5\49 122.449 48.980 5:2 2.500 Semihard 7L 7s
13\126 123.810 47.619 13:5 2.600
8\77 124.675 46.753 8:3 2.667
11\105 125.714 45.714 11:4 2.750
3\28 128.571 42.857 3:1 3.000 Hard 7L 7s
10\91 131.868 39.560 10:3 3.333
7\63 133.333 38.095 7:2 3.500
11\98 134.694 36.735 11:3 3.667
4\35 137.143 34.286 4:1 4.000 Superhard 7L 7s
9\77 140.260 31.169 9:2 4.500
5\42 142.857 28.571 5:1 5.000
6\49 146.939 24.490 6:1 6.000
1\7 171.429 0.000 1:0 → ∞ Collapsed 7L 7s

Scale tree

Scale tree and tuning spectrum of 7L 7s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\14 85.714 85.714 1:1 1.000 Equalized 7L 7s
6\77 93.506 77.922 6:5 1.200
5\63 95.238 76.190 5:4 1.250
9\112 96.429 75.000 9:7 1.286
4\49 97.959 73.469 4:3 1.333 Supersoft 7L 7s
11\133 99.248 72.180 11:8 1.375
7\84 100.000 71.429 7:5 1.400
10\119 100.840 70.588 10:7 1.429
3\35 102.857 68.571 3:2 1.500 Soft 7L 7s
11\126 104.762 66.667 11:7 1.571
8\91 105.495 65.934 8:5 1.600
13\147 106.122 65.306 13:8 1.625
5\56 107.143 64.286 5:3 1.667 Semisoft 7L 7s
12\133 108.271 63.158 12:7 1.714
7\77 109.091 62.338 7:4 1.750
9\98 110.204 61.224 9:5 1.800
2\21 114.286 57.143 2:1 2.000 Basic 7L 7s
9\91 118.681 52.747 9:4 2.250
7\70 120.000 51.429 7:3 2.333
12\119 121.008 50.420 12:5 2.400
5\49 122.449 48.980 5:2 2.500 Semihard 7L 7s
13\126 123.810 47.619 13:5 2.600
8\77 124.675 46.753 8:3 2.667
11\105 125.714 45.714 11:4 2.750
3\28 128.571 42.857 3:1 3.000 Hard 7L 7s
10\91 131.868 39.560 10:3 3.333
7\63 133.333 38.095 7:2 3.500
11\98 134.694 36.735 11:3 3.667
4\35 137.143 34.286 4:1 4.000 Superhard 7L 7s
9\77 140.260 31.169 9:2 4.500
5\42 142.857 28.571 5:1 5.000
6\49 146.939 24.490 6:1 6.000
1\7 171.429 0.000 1:0 → ∞ Collapsed 7L 7s


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